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Prove the Following by Using the Principle of Mathematical Induction for All N ∈ N: 1 + 3 + 3^2 + ... + 3^(N – 1) =((3^N -1))/2 - CBSE (Arts) Class 11 - Mathematics

ConceptPrinciple of Mathematical Induction

Question

Prove the following by using the principle of mathematical induction for all n ∈ N

1 + 3 + 3^2 + ... + 3^(n – 1) =((3^n -1))/2

Solution

Let the given statement be P(n), i.e.,

= (3^(k+1) - 1)/2

Thus, P(k + 1) is true whenever P(k) is true.

Hence, by the principle of mathematical induction, statement P(n) is true for all natural numbers i.e., n.

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NCERT Solution for Mathematics Textbook for Class 11 (2018 to Current)
Chapter 4: Principle of Mathematical Induction
Q: 1 | Page no. 94

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Solution Prove the Following by Using the Principle of Mathematical Induction for All N ∈ N: 1 + 3 + 3^2 + ... + 3^(N – 1) =((3^N -1))/2 Concept: Principle of Mathematical Induction.
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